What are the solutions to the equation r^5=8r^2 ?

The solutions to the equation r^5=8r^2 are r=0,r=2,r=-1+sqrt(3)i,r=-1-sqrt(3)i

Find the zeros of r^5=8r^2

The zeros of r^5=8r^2 are r=0,r=2,r=-1+sqrt(3)i,r=-1-sqrt(3)i

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r^{5} = 8 r^{2}

r = 0, r = 2, r = - 1 + 3 i, r = - 1 - 3 i

Solution steps

r^{5} = 8 r^{2}

Move

8 r^{2}

to the left side

r^{5} - 8 r^{2} = 0

Factor

r^{5} - 8 r^{2} : r^{2} (r^{3} - 8)

r^{2} (r^{3} - 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

r = 0 or r^{3} - 8 = 0

Solve

r^{3} - 8 = 0 : r = 2, r = - 1 + 3 i, r = - 1 - 3 i

The solutions are

r = 0, r = 2, r = - 1 + 3 i, r = - 1 - 3 i

y, y^{3} = x^{3} + 4 x^{4} - x^{5} + 2 x^{2} - x + 1

(5 - 2 x)^{3} = - 27

3 x^{4} = 9

x^{4} - 9 = 2 x^{4} + 6 x^{2}

x^{3} - 14 x^{2} - 49 = 0

What are the solutions to the equation r^5=8r^2 ?
The solutions to the equation r^5=8r^2 are r=0,r=2,r=-1+sqrt(3)i,r=-1-sqrt(3)i
Find the zeros of r^5=8r^2
The zeros of r^5=8r^2 are r=0,r=2,r=-1+sqrt(3)i,r=-1-sqrt(3)i